Correlation Squared
This is the classical statistical method for measuring how closely related the variances of two series are. The correlation is defined as:
More explicitly, this is:
where
n = number of returns
bi = i-th benchmark return
mi = i-th manager return
= average benchmark return
= average manager return
The correlation squared is of course the square of the above expression.
(covariance of manager and benchmark)
(standard deviation of manager) * (standard deviation of benchmark)
(standard deviation of manager) * (standard deviation of benchmark)
More explicitly, this is:
where
n = number of returns
bi = i-th benchmark return
mi = i-th manager return
= average benchmark return= average manager returnThe correlation squared is of course the square of the above expression.